Stopping power is an armchair philosophy about the degree to which a given caliber or bullet can quickly incapacitate or immobilize (or kill) an attacker.
Stopping power is not something that can really be quantified* due to the very large number of variables in predicting terminal ballistics. These mainly have to do with where a target is struck, which vital organs have been damaged, whether bones or clothing have limited penetration, and even the physical size of the target. A bullet fired from an anemic cartridge that strikes the central nervous system is going to stop an assailant more effectively than a gut shot from a powerful cartridge. The FBI has created testing standards for firearm ammunition to measure bullet penetration and expansion in ballistic gelatin and through a variety of barriers, but the very nature of these tests serves as an acknowledgement of what cannot be predicted in the real world.
Attempts have been made to use real world data to draw statistical conclusions about different types of firearm cartridges. Unfortunately, the pool of usable is very is rather small and of poor quality. One popular attempt (Marshall/Sanow) has been to use police shooting data to quantify “one-shot stop” percentages by caliber/bullet, but the value of their findings was limited at the time, and is now dated.
Ultimately, stopping power mostly comes down to an individual’s arbitrary confidence in a particular caliber or bullet design, which tends to be influenced more by theory and myth and the sensation of shooting a given gun than by actual data.
(* Though, people have certainly tried. See the Taylor knock-out factor, for example.)